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Simplifying n2 + 6n + -77 = 0 Reorder the terms: -77 + 6n + n2 = 0 Solving -77 + 6n + n2 = 0 Solving for variable 'n'. Begin completing the square. Move the constant term to the right: Add '77' to each side of the equation. -77 + 6n + 77 + n2 = 0 + 77 Reorder the terms: -77 + 77 + 6n + n2 = 0 + 77 Combine like terms: -77 + 77 = 0 0 + 6n + n2 = 0 + 77 6n + n2 = 0 + 77 Combine like terms: 0 + 77 = 77 6n + n2 = 77 The n term is 6n. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6n + 9 + n2 = 77 + 9 Reorder the terms: 9 + 6n + n2 = 77 + 9 Combine like terms: 77 + 9 = 86 9 + 6n + n2 = 86 Factor a perfect square on the left side: (n + 3)(n + 3) = 86 Calculate the square root of the right side: 9.273618495 Break this problem into two subproblems by setting (n + 3) equal to 9.273618495 and -9.273618495.Subproblem 1
n + 3 = 9.273618495 Simplifying n + 3 = 9.273618495 Reorder the terms: 3 + n = 9.273618495 Solving 3 + n = 9.273618495 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + n = 9.273618495 + -3 Combine like terms: 3 + -3 = 0 0 + n = 9.273618495 + -3 n = 9.273618495 + -3 Combine like terms: 9.273618495 + -3 = 6.273618495 n = 6.273618495 Simplifying n = 6.273618495Subproblem 2
n + 3 = -9.273618495 Simplifying n + 3 = -9.273618495 Reorder the terms: 3 + n = -9.273618495 Solving 3 + n = -9.273618495 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + n = -9.273618495 + -3 Combine like terms: 3 + -3 = 0 0 + n = -9.273618495 + -3 n = -9.273618495 + -3 Combine like terms: -9.273618495 + -3 = -12.273618495 n = -12.273618495 Simplifying n = -12.273618495Solution
The solution to the problem is based on the solutions from the subproblems. n = {6.273618495, -12.273618495}
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